London -LRB- CNN -RRB- -- Peaches Geldof , the daughter of musician Bob Geldof and the late Paula Yates , died of a heroin overdose after relapsing into use of the illegal drug following attempts to give it up , an inquest heard Wednesday .

The death of the 25-year-old TV host in April at her home in Wrotham , Kent , southeast of London , shocked the entertainment world .

Detective Chief Inspector Paul Fotheringham of Kent police told the inquest that Geldof had been addicted to heroin for a number of years but had ceased taking the drug more recently .

Geldof , who had two children younger than 2 , had been supported by drug treatment workers for 2Â 1/2 years , being prescribed methadone , he said . She had said she wanted to come off methadone completely and was following a reduction plan .

A drug test in November indicated that she was not taking any illegal drugs , he said . However , in February , witnesses reported suspicions that she had started using heroin again .

High-grade heroin

Fotheringham 's report to the inquest gave new details of Geldof 's death .

Police who searched the house where she died found a black cloth bag hidden in a cupboard above the door of a spare bedroom , he said .

Inside was a bag containing what tests proved to be heroin as well as a bag of citric acid , used to make the heroin more soluble in water for injection , according to the report . The bag also held dozens of syringes , some sealed while others contained traces of a brown residue , alcohol wipes , cotton buds and cards advertising a needle exchange in central London .

According to a police drug expert , PC Adrian Parsons , the heroin found was of `` importation quality '' -- that is , with a purity of 61 % , compared with the average 26 % purity found at street level .

The 6.91 grams -LRB- about a quarter-ounce -RRB- recovered would have been worth Â # 350 to Â # 550 -LRB- about $ 600 to $ 940 -RRB- , Fotheringham said .

Burnt spoon , knotted tights

Geldof was discovered sitting slumped on a bed in the spare bedroom by her husband , rock musician Tom Cohen , who went to their home after he became concerned when he could n't contact her .

The couple 's younger son , Phaedra , was in the house at the time , having been dropped off by Cohen 's father the previous afternoon . The musician had taken both children to spend the weekend at his parents ' home .

A pair of knotted black tights was found under her body , and a burnt spoon containing a small amount of a brown residue in the bowl was found under the bed , Fotheringham said . The tights could have been used as a tourniquet while she was injecting the drug .

An autopsy also found evidence of recent puncture marks on the inside of both elbows and on her left hand .

The inquest heard that tests by a forensic scientist suggested recent use of the drug , resulting in a `` high '' concentration of heroin in Geldof 's body , which was `` at the end of the range of values at which fatalities have occurred . ''

She was not under the influence of alcohol at the time of her death , tests revealed . Nor had she taken a significant amount of any other substances in the hours leading up to her death .

Reduced tolerance ?

The scientist 's report notes that people using heroin regularly `` develop a tolerance to the drug , and such individuals can use doses that would be toxic , or fatal , to people with no tolerance . ''

But it adds that tolerance `` appears to be lost fairly rapidly when users cease to use the drug , and deaths commonly occur in people who have previously been tolerant and have returned to using heroin . ''

Fotheringham 's report concluded , `` There is no indication that any other third party was present or involved in her death and there is no indication that Peaches intended to take her own life or harm herself in any way as she was reported to be of happy disposition and planning for the future with friends and family . ''

Geldof was 11 years old when her mother died of a drug overdose .

Kent police continue to investigate who supplied the heroin to Geldof , but no arrests have been made .

CNN 's Carol Jordan contributed to this report .

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NEW : Puncture marks found on Peaches Geldof 's arms and one hand , an inquest hears

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Geldof had been addicted to heroin for a number of years but tried to give it up

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She had been on a methadone program , an inquest hears

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Police found heroin in her home of a much greater purity than average found on the street